I am trying to sell 150 shares of stock that I received as a gift from
a relative.  The stock is all in certificate form.  After Googling for
awhile, the only option that I can find is that I go to a broker,
present him (or her) with my stock certificates, and have him (or her)
sell them for me.

My question is this: can I, for example, go to Charles Schwab, give
the broker my certificates, have him sell them for me, pay the fee or
commission, and never go back again?  That is to say, must I open a
brokerage account in order to sell these certificate shares, or can I
just walk in, sell, pay the fee, and walk out?

Any advice is appreciated.

Hello.

Yes, Charles Schwab does in fact offer the exact service that you seek.

They call it the "Schwab Stock Liquidation Service" (i.e., a temporary
account for a one-time transaction by a non-client).

The application for this service states:

"Use this account to sell your stock certificates.
The Stock Liquidation Service is for non-Schwab clients only.
This account is intended for a one-time-only transaction." 

Download the application and instructions here:
http://www.schwab.com:80/public/file?cmsid=P-221964&filename=stk_liquidation_instr.pdf

(This document is in PDF format, so the Adobe Acrobat Reader is
required. If you don't have that, visit:
http://www.adobe.com/products/acrobat/readstep2.html )


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search strategy:
schwab "stock liquidation"

Good luck!

Thank you so much, juggler, for your reply.  You saved me lots and
lots and lots of searching.  I appreciate your help.

If the name on the certificates is not yours, being a gift, you will
need documentation of your ownership.

Myoarin: Thank you for your clarification, but I was unclear myself. 
The shares were actually transferred to me and new certificates, with
my name on them, were drawn up.  (As you can see, this is all very new
to me!)